Alexa ranking has no influence on ranking on the SERPs... In otherwords it is not a ranking factor... It is a commercially owned outfit and is actually owned by Amazon and as such have their own profit making agenda.. Some people seem to think their are some form of independent organisation like the UN, but that is not the case lol... They may have some useful metrics but its all estimates and for me I dont take any of it seriously...
Its worth noting that Alexa in recent months has increased its number of websites and hence the massive change in rankings... So its nothing to worry about, especially given your traffic numbers are increasing....
I think alexa ranking can be easily altered through purchasing massive traffic. Don't ever trust it when buying a website, don't judge it by that straight away. Anyway, maybe its just fluctuating, is your site new?
Many shady websites allow the purchase of millions of visitors for cheap, these visitors are useless.
Fiverr has many people selling those services, google purchase visitors. I think they get this traffic from ptc sites which gets a huge amount of visitors to your website.
Analytics simply track the number of visitors come to your website.
On the other side Alexa of your website depends upon the number of visitors plus the quality links which show on alexa, when you check website on alexa website.